Enhanced Lasso Recovery on Graph

This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on graphs. More precisely, we present a non-convex, non-smooth algorithm that outperforms the standard convex Lasso technique. We carry out numerical experiments on three benchmark graph datasets

ECONOMIC EFFECTS OF POSSIBLE EUROPEAN COMMUNITY MARKET INTERVENTION IN SOYBEANS AND THEIR PRODUCTS

Crop Production/Industries, International Relations/Trade,

Earth's Energy Imbalance and Implications

Improving observations of ocean heat content show that Earth is absorbing more energy from the sun than it is radiating to space as heat, even during the recent solar minimum. The inferred planetary energy imbalance, 0.59 \pm 0.15 W/m2 during the 6-year period 2005-2010, confirms the dominant role of the human-made greenhouse effect in driving global climate change. Observed surface temperature change and ocean heat gain together constrain the net climate forcing and ocean mixing rates. We conclude that most climate models mix heat too efficiently into the deep ocean and as a result underestimate the negative forcing by human-made aerosols. Aerosol climate forcing today is inferred to be 1.6 \pm 0.3 W/m2, implying substantial aerosol indirect climate forcing via cloud changes. Continued failure to quantify the specific origins of this large forcing is untenable, as knowledge of changing aerosol effects is needed to understand future climate change. We conclude that recent slowdown of ocean heat uptake was caused by a delayed rebound effect from Mount Pinatubo aerosols and a deep prolonged solar minimum. Observed sea level rise during the Argo float era is readily accounted for by ice melt and ocean thermal expansion, but the ascendency of ice melt leads us to anticipate acceleration of the rate of sea level rise this decade.Comment: 39 pages, 18 figures; revised version submitted to Atmos. Chem. Phy

From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps

In CMB science, the simplest idea to remove a contaminated sky region is to multiply the sky map with a mask that is 0 for the contaminated region and 1 elsewhere, which is also called a top-hat masking. Although it is easy to use, such top-hat masking is known to suffer from various leakage problems. Therefore, we want to extend the top-hat masking to a series of semi-analytic functions called the P-filters. Most importantly, the P-filters can seamlessly realize the core idea of masking in CMB science, and, meanwhile, guarantee continuity up to the first derivative everywhere. The P-filters can significantly reduce many leakage problems without additional cost, including the leakages due to low-, high-, and band-pass filtering, and the E-to-E, B-to-B, B-to-E, and E-to-B leakages. The workings of the P-filter are illustrated by using the WMAP and Planck polarization sky maps. By comparison to the corresponding WMAP/Planck masks, we show that the P-filter performs much better than top-hat masking, and meanwhile, has the potential to supersede the principal idea of masking in CMB science. Compared to mask apodization, the P-filter is ``outward'', that tends to make proper use of the region that was marked as 0; whereas apodization is ``inward'', that always kills more signal in the region marked as 1.Comment: 19 pages and 11 figure

Visualizing Interstellar's Wormhole

Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities, including: (i) At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations seen in the movie. (ii) At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie. (iii) Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera's local sky to a wormhole's two celestial spheres. (iv) Implementing this map, for example in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole. (v) With the student's implementation, exploring how the wormhole's three parameters influence what the camera sees---which is precisely how Christopher Nolan, using our implementation, chose the parameters for \emph{Interstellar}'s wormhole. (vi) Using the student's implementation, exploring the wormhole's Einstein ring, and particularly the peculiar motions of star images near the ring; and exploring what it looks like to travel through a wormhole.Comment: 14 pages and 13 figures. In press at American Journal of Physics. Minor revisions; primarily insertion of a new, long reference 15 at the end of Section II.